In this paper, we consider the OPE of the non-local operator in Eq. (REF ) to three-loop accuracy, taking
into account all scalar operators up to dimension four. As a by-product of this calculation,
the three-loop AD (matrix) of the non-local gluon operator is obtained. From the technical
point of view, this calculation is an extension of our work in Ref. [1]}, where the perturbative
contribution to the OPE was calculated to three-loop accuracy and the two-loop AD was derived. We will mostly adopt
the conventions and the notation of Ref. [1]}, a short summary of which is given in Sect. 2. The calculation is described
in Sect. 3. The results for the relevant ADs and coefficient functions (CFs) are presented in Sect. 4.
The renormalization group (RG) evolution equations for the computed CFs as well as the RG improvement of the purely perturbative contributions are considered in Sects. 5 and 6.
Section 7 is reserved for a summary and conclusions.
